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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</a>;<br/><b>let </b><font color="Maroon" title="c2">I</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>



<b>assume </b><a NAME="E1:158"/><i><font color="Green" title="E98">A1</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="aofa_000.html#D36" target="_self" title="AOFA_000:def.36">AOFA_000:def 36</a><br/>

<b>thus </b><a NAME="E2:158"/>
for <font color="Olive" title="b1">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b3">f</font> being   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">S</font>,<font color="Olive" title="b2">T</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">I</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_000.html#K21" title="AOFA_000:func.21">TerminatingPrograms</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">S</font>,<font color="Olive" title="b2">T</font>,<font color="Olive" title="b3">f</font>
 <b>by </b><i><a class="txt" href="aofa_000.html#E1:158"><i><font color="Green" title="E98">A1</font></i></a>, <a class="ref" href="aofa_000.html#T94" target="_self" title="AOFA_000:th.94">Th94</a></i>;<br/>


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